For Dung's theory of abstract argumentation, algorithms have been introduced for enumerating all preferred extensions. Two specific approaches have been set out that are based on labeling arguments as: IN, OUT or UNDEC. The purpose of this paper is to improve the two existing approaches by introducing two enhancements. Firstly, we employ two more informative labels. Secondly, by using these additional labels, we describe a new scheme for how the arguments' labels change in the course of computing the preferred extensions. Supported by empirical evaluation, we argue that these modifications accelerate computations. Moreover, we show how to apply the new algorithm in the context of value-based frameworks for persuasive argument, and hence, it appears that the new algorithm is usable in other formalisms extending Dung's model.